论文标题
用尖尖的几何双曲线歧管的测地层的指数混合
Exponential mixing of geodesic flows for geometrically finite hyperbolic manifolds with cusps
论文作者
论文摘要
令$γ$作为$ \ operatatorName {so}（d+1,1）^{\ circ} $的几何离散子组，带有抛物线元素。我们在单元切线捆绑$ \ operatorName {t}^1（γ\ backslash \ mathbb {h}^{d+1}）$上建立了测量流的指数混合\ mathbb {h}^{d+1}）$带有最大熵。作为一个应用程序，我们在$γ\ backslash \ mathbb {h}^{d+1} $上获得了Laplacian分解的无共振区域。我们的方法是构建用于测量流的编码，然后证明对相应的传输操作员进行dolgopyat-type频谱估计。
Let $Γ$ be a geometrically finite discrete subgroup in $\operatorname{SO}(d+1,1)^{\circ}$ with parabolic elements. We establish exponential mixing of the geodesic flow on the unit tangent bundle $\operatorname{T}^1(Γ\backslash \mathbb{H}^{d+1})$ with respect to the Bowen-Margulis-Sullivan measure, which is the unique probability measure on $\operatorname{T}^1(Γ\backslash \mathbb{H}^{d+1})$ with maximal entropy. As an application, we obtain a resonance free region for the resolvent of the Laplacian on $Γ\backslash \mathbb{H}^{d+1}$. Our approach is to construct a coding for the geodesic flow and then prove a Dolgopyat-type spectral estimate for the corresponding transfer operator.
